mock exam 5 mc · 2019. 1. 9. · mock exam 5 mathematics compulsory part paper 2 (1 4 1 hours)...

MOCK EXAM 5

MATHEMATICS Compulsory Part

PAPER 2

(14

1 hours)

INSTRUCTIONS

1. Read carefully the instructions on the Answer Sheet.

2. When told to open this book, you should check that all the questions are there. Look for the words

‘END OF PAPER’ after the last question.

3. All questions carry equal marks.

4. ANSWER ALL QUESTIONS. You are advised to use an HB pencil to mark all the answers on the

Answer Sheet, so that wrong marks can be completely erased with a clean rubber. You must mark

the answers clearly; otherwise you will lose marks if the answers cannot be captured.

5. You should mark only ONE answer for each question. If you mark more than one answer, you will

receive NO MARKS for that question.

6. No marks will be deducted for wrong answers.

https://www.brightmind.com.hk 5500 1376 All Rights Reserved 2

Mock exam paper 5

There are 30 questions in Section A and 15 questions in Section B.

The diagrams in this paper are not necessarily drawn to scale.

Choose the best answer for each question.

Section A

1. (x – 1)(x

2 – x + 1) =

A. x3 – 1.

B. (x – 1)3.

C. x3 – x

2 + x – 1.

D. x3 – 2x

2 + 2x – 1.

2. 62

4

)2(

2

x

x=

A. 26

1

x.

B. 46

1

x.

C. 332

1

x.

D. 832

1

x.

3. If 2p + 3q = 3 and 3p + 5q = 7, then p =

A. –6.

B. –3.

C. 3.

D. 6.

https://www.brightmind.com.hk/


Mock exam paper 5

4. Let f(x) = x3 + x

2 + kx + 9. If x + 3 is a factor of f(x), then k =

A. –15.

B. –9.

C. –3.

D. 3.

5. If a > b and k < 0, which of the following must be true?

I. ak2 > bk

2

II. a2 > b

2

III. a – k > b – k

A. I only

B. II only

C. I and III only

D. II and III only

6. The solution of 7 – 2x < 9 or 3x + 8 > –1 is

A. x > –3.

B. x > –1.

C. x > 1.

D. –3 < x < –1.

7. The figure shows the graph of y = x2 – mx + n, where m and n are constants. Which of the following is

true?

A. m < 0 and n > 0

B. m < 0 and n < 0

C. m > 0 and n > 0

D. m > 0 and n < 0

y

Go on to the next page

x O

y = x2 – mx + n



Mock exam paper 5

8. If α is a root of the equation 5x2 – 2x + 4 = 0, then 1 + 6α – 15α2 =

A. 11.

B. 13.

C. 15.

D. 17.

9. If the price of a car is increased by 80% and then decreased by 70%, find the percentage change in the

price of the car.

A. –46%

B. –44%

C. 10%

D. 26%

10. In a factory, 54.5% of the workers are male. If 75% of the female workers and 50% of the male workers

are married, then find the number of unmarried workers given that there are 273 married female

workers.

A. 218

B. 273

C. 309

D. 364

11. Let a, b and c are non-zero numbers. If a : b = 5 : 8 and a : c = 3 : 4, then (b – a) : (c – a) =

A. 3 : 1.

B. 9 : 5.

C. 6 : 5.

D. 5 : 9.



Mock exam paper 5

12. In the figure, the 1st pattern consists of 3 dots. For any positive integer n, the (n + 1)th pattern is formed

by adding n + 2 dots to the nth pattern. Find the number of dots in the 6th pattern.

A. 21

B. 28

C. 30

D. 36

13. 0.002016789 =

A. 0.002016 (correct to 6 decimal places).

B. 0.002017 (correct to 6 decimal places).

C. 0.002017 (correct to 6 significant figures).

D. 0.00201678 (correct to 6 significant figures).

14. There are packets of salt. The weight of salt in a packet is measured as 100 g correct to the nearest g. If

n packets of salt are packed into a bag such that the weight of salt in each bag is measured as 15 kg

correct to the nearest kg, find the least possible value of n.

A. 144

B. 145

C. 150

D. 155

15. It is given that z varies directly as x2 and inversely as y

3. When x = 2 and y = 1, z = 32. When x = –1

and y = 2, z =

A. –32.

B. –1.

C. 1.

D. 32.




Mock exam paper 5

16. In the figure, F is a point lying on BD. If EF = 8 cm and AF = BF, then the area of ΔBCD is

A. 24 cm2.

B. 60 cm2.

C. 84 cm2.

D. 168 cm2.

17. In the figure, ABCD is a parallelogram. E is a point lying on CD such that DE : EC = 4 : 3. AE

produced and BC produced meet at F. If the area of ΔCEF is 18 cm2, then the area of the parallelogram

ABCD is

A. 72 cm2.

B. 80 cm2.

C. 98 cm2.

D. 112 cm2.

18. In the figure,CD

AB=

A.

cos

cos.

B.

sin

sin.

C. sin αsin β.

D. cos αcos β.

A

B C

D

E

F

A

B

D C

E

F

6 cm

17 cm

24 cm

B C

A D



Mock exam paper 5

19. )270sin(1

330sin

)90sin(1

150sin

o

o

o

o

=

A. 0.

B. cos

1.

C. 2sin

1.

D.

2sin

cos.

20. In the figure, O is the centre of the circle ABCD. If ∠BAD = 80o, ∠ADO = 25o and AB = BC, then

∠COD =

A. 90o.

B. 100o.

C. 105o.

D. 115o.

21. The chords AC and BD of the circle ABCD intersect at the point E. If ∠AEB = 90o, CE = 3 cm,

DE = 4 cm and BD = 10 cm, then the area of ΔAEB is

A. 6 cm2.

B. 12 cm2.

C. 24 cm2.

D. 48 cm2.

C

A

O

B


D

80o

25o



Mock exam paper 5

22. If an interior angle of a regular polygon is larger than an exterior angle of the polygon by 90o, which of

the following is/are true?

I. Each interior angle of the polygon is 135o.

II. The number of diagonals of the polygon is 16.

III. The number of folds of rotational symmetry is 8.

A. I only

B. II only

C. I and III only

D. II and III only

23. The rectangular coordinates of the point P are (1, – 3 ). If P is reflected with respect to the y-axis, then

the polar coordinates of its image are

A. (1, 210o).

B. (1, 240o).

C. (2, 210o).

D. (2, 240o).

24. If P is a moving point in the rectangular coordinate plane such that the distance between P and the point

(2, 6) is equal to 10, then the locus of P is a

A. circle.

B. straight line.

C. parabola.

D. square.

25. If a diameter of the circle x2 + y

2 + kx – 14y + 45 = 0 passes through the points (–3, 9) and (5, 5), then

k =

A. –5.

B. –2.

C. 1.

D. 7.



Mock exam paper 5

26. In the figure, the equations of the straight lines L1 and L2 are cy = 1 and ax + by = 1 respectively.

Which of the following are true?

I. c < 0

II. b < c

III. a > 0

A. I and II only

B. I and III only

C. II and III only

D. I, II and III

27. A fair coin is thrown three times in a game. If 3 heads are obtained, 80 tokens will be awarded;

otherwise, 8 tokens will be awarded. Find the expected number of tokens of the game.

A. 17

B. 18

C. 70

D. 71

28. The bar chart below shows the distribution of the number of bags owned by a group of girls. Find the

probability that a randomly selected girl from the group owns less than 2 bags.

A. 5

1

B. 14

5

C. 7

3

D. 14

11


x O

y

L1

L2

0

2

4

6

8

10

0 1 2 3 4 Number of bags

Number of girls



Mock exam paper 5

29. The box-and-whisker diagram drawn below shows the distribution of the temperatures in a month. Find

the inter-quartile range of the distribution.

A. 4 oC

B. 5 oC

C. 7 oC

D. 9 oC

30. Consider the following integers:

11 12 12 13 14 14 14 14 16 16 19 19 20 20 20 21 k

Let a, b and c be the mean, the median, and the mode of the above integers respectively. If 14 k16,

which of the following must be true?

I. a > c

II. b > c

III. a > b

A. I only

B. II only

C. I and III only

D. II and III only

22 24 26 28 30 32 34 Temperature (

oC)



Mock exam paper 5

Section B

31. 65

12 xx

+127

12 xx

=

A. )3)(2(

2

xx.

B. )4)(3(

2

xx.

C. )4)(2(

2

xx.

D. )4)(3)(2(

6

xxx

x.

32. The graph in the figure shows the linear relation between log4 y and x. If y = mnx, then m =

A. 3.

B. 4.

C. 12.

D. 64.

33. 21 + 27 + 2

8 + 2

12 =

A. 10001100101012.

B. 10011010101012.

C. 100001100101012.

D. 100011010101012.

34. Let k be a constant. If the roots of the quadratic equation x2 – kx – 4 = 0 are α and β, then α3 +β3 =

A. k3.

B. k3 + 8k.

C. k3 + 12k.

D. k3 – 12k.


x O

3

log4 y



Mock exam paper 5

35. Let f(x) = 4x2 + kx + 20, where k is a constant. If the y-coordinate of the vertex of the graph of y = f(x)

is 16, then k =

A. 4.

B. 4 or –4.

C. 8 or –8.

D. 16 or –16.

36. If k is a real number, then 5k –i

ki4=

A. 4k + 4i.

B. 4k – 4i.

C. 6k + 4i.

D. 6k – 4i.

37. The nth term of a sequence is 3n – 28. Which of the following is/are true?

I. –16 is a term of the sequence.

II. The sequence has 8 negative terms.

III. The sum of the first n terms of the sequence is 2

533 2 nn .

A. I only

B. II only

C. I and III only

D. II and III only

38. For 0ox360

o, how many roots does the equation 3cos

2 x + sin x = 3 have?

A. 2

B. 3

C. 4

D. 5



Mock exam paper 5

39. Let k be a positive constant and –90o < θ < 90o. If the figure shows the graph of y = cos(kxo +θ),

then

A. k = 2 ,θ= 65o .

B. k = 2 ,θ= –65o.

C. k =2

1,θ= 65o.

D. k =2

1,θ= –65o .

40. In the figure, O is the centre of the circle PQR. If PORS is a straight line and QS is a tangent to the

circle with radius 3 cm, find the length of QS.

A. 1.5 cm

B. 3 cm

C. 2 3 cm

D. 3 3 cm

41. Find the values of k such that the circle x2 + y

2 + kx – 4y + 6 = 0 and the straight line x – y + 6 = 0

intersect at only one point.

A. 4 or –20

B. 4 or 20

C. –4 or 20

D. –4 or –20

42. Let O be the origin. If the coordinates of points A and B are (0, 36) and (24, 0) respectively, then the

x-coordinate of the circumcentre of △OAB is

A. 12.

B. 18.

C. 24.

D. 36.

y


x O 410 50

Q

R P

O

30o

S



Mock exam paper 5

43. Amy and Bill form a queue with 7 other students. If Amy and Bill are not next to each other, how many

different queues can be formed?

A. 10 080

B. 80 640

C. 282 240

D. 322 560

44. Bag A contains 4 red balls, 4 green balls and 3 blue balls while bag B contains 2 red balls, 5 green balls

and 4 brown balls. If one ball is drawn from each bag, then the probability that the two balls drawn are

of different colours is

A. 121

28.

B. 121

40.

C. 121

61.

D. 121

93.

45. Let x1, y1 and z1 be the median, the inter-quartile range and the standard deviation of a group of

numbers {a, b, d, e} respectively while x2, y2 and z2 be the median, the inter-quartile range and the

standard deviation of a group of numbers {a + 1, b + 1, c + 1, d + 1, e + 1} respectively where

a < b < c < d < e. Which of the following must be true?

I. x1 < x2

II. y1 = y2

III. z1 > z2

A. I and II only

B. I and III only

C. II and III only

D. I, II and III only

END OF PAPER

mock exam 5 mc · 2019. 1. 9. · mock exam 5 mathematics compulsory part paper 2 (1 4 1 hours)...

Documents